This is the worst offender of the whole achievements system. As I previously stated, a game already has its own motivators -- in fact, the purpose of a game designer is balancing motivators around a goal to create the intended gameplay experience.
But some achievements actually influence players to act in ways that they would not normally act. I remember this kind of thing happening a lot in Team Fortress 2. Often there would be a medic doing something really stupid instead of healing teammates. Angrily, I'd ask, "What the hell are you doing, dude? Heal us."
"I'm going for an achievement", he'd reply.
This is really not that rare an occurrence, particularly when a game is new. We now have a situation where players are actively not playing correctly and disturbing or ruining the game experience for other players because of achievements.
A common mistake would be to blame this on that player. Let's put it this way: if you're blaming a player for wanting to make use of the system of achievements, then you're proving my point even further that they need to go.
Here's an example of such a behavior-influencing achievement in CS: GO:
"Second to None - successfully defuse a bomb with less than one second remaining"
It's not too hard to imagine that many a game have already been lost by a player miscalculating when he should start the defuse and having it take too long, or by waiting a few seconds before defusing only to be shot right at the end of the defuse. This sucks for the other players on the team. Remember, the goals of a game should be agreed upon by all participating parties.
My Suggested Replacement: Variants!
Is there anything salvageable to this whole mess? Yes, there is. Some of the achievements -- those most-offensive ones that influence behavior, specifically -- have the potential to be interesting variants. While I don't expect achievements to vanish or dramatically change overnight, variants provide an alternative route that should be explored either in their place, or in addition to achievements.
What's the big difference between variants and achievements? A variant would be a new goal that you actively choose before the game begins, and only that single chosen "goal" is active during this session. One of the fundamental aspects of "a game" is that the rules and goals are agreed upon before the game begins. It doesn't make any sense to allow players to choose what their goals are on the fly, in the middle of the game. This will just allow them to choose whichever goal is most doable based on "how things are going". Worse, if you allow all the goals to be active at once, goals are going to be met by accident.
In Nethack, variants are referred to as "conducts." From the Nethack Wikipedia page,
These are voluntary restrictions on actions taken, such as using no wishes, following a vegetarian or even vegan diet, or even killing no monsters.
In Counter-Strike, being a multiplayer game, variants would have to affect all players. It would be strange if the Terrorist team won, but one of the terrorists lost because he had activated some special variant that said he wasn't allowed to take grenade damage, or something. Technically, there's nothing wrong with this, as long as all players agree to it beforehand, but it's messy and strange.
Instead, better Counter-Strike variants are already seen on public servers. Things like "No AWP/Auto", or "Infinite money", or "Betting" would all count as variants. These pose a new challenge to players -- "can you win this match when the AWP is disabled?" There are other more otherworldly server-variants that add RPG elements, zombies, and other rules.
Look at this achievement from XCOM, and tell me that it isn't a full-fledged variant waiting to happen:
"Lone Wolf - Clear a UFO crash site with one soldier on Classic or Impossible difficulty."
Why We Use Achievements
As a developer myself, I think that there's this feeling like "the audience expects achievements, so let's humor them." I suspect that players probably feel a similar way; something like "oh, well, the developers like to put in achievements for some reason, so let's humor them." In other words, few people actually like achievements, but everyone believes that everyone else likes them, so they continue to exist.
I also think that it's continued to exist because, if we're being honest, a lot of video games these days are not terribly interesting on their own. The thinking is that developers can use the cheap distraction / lame collection-game that achievements provide to create interest in an otherwise uninteresting system. Their primary function, much of the time, is to stretch out what little interest there is over a larger amount of time by compelling the player to "collect". They stand out the most when they're in a game that doesn't need that – a game like Counter-Strike: Global Offensive.
It's important not to fall into the trap of thinking that just because we've had achievements for over half a decade that we will always have them. Now, I'll definitely acknowledge that there is indeed a chance that we will always have them, at least in some form, but it's worth noting that Nintendo has made a point of not using such a system, and that hasn't seemed to affect their commercial or critical success. As I've pointed out, there are a number of flaws with the achievements model, and as time goes on, what I am certain of is that they will either change drastically or disappear.
If you're a fan of achievements, I would simply ask that you try to look at them with a fresh perspective and ask what it is they really do for your software, and whether or not the points I've raised creates issues for it.
So look -- people expect "metagame," and I understand that. But if you have great metagame in the form of variants, great networking (such as cutting-edge, smart online leaderboards), as well as additional gameplay content, the number of people who flip out because you don't have "achievements" will be negligible. At some point, people will stop expecting them, as quickly as they learned to expect them in the first place.